PLEASE SHOW ALL WORK!!! THANK YOU!!! Consider the system of equations: Exress th

Question

PLEASE SHOW ALL WORK!!! THANK YOU!!!

Consider the system of equations: Exress this system in vector form, .Ax = b. Determine the solution set of the homogeneous system .Ax = 0. Determine all right-hand-side vectors. for which the linear system .Ax = b is consistent. (HINT: Find a condition on the entries in the vector b.) A scientist determines that a non-homogeneous system of ten linear equations in twelve unknowns is consistent and three of the unknowns are free variables. Determine the dimensions and the rank of the augmented matrix of the system. If the right-hand-side vector is changed, is the resulting system of linear equations still consistent? Explain.

Explanation / Answer

a.

Ax= b

matrix A matrix x = matrix b

1 1 1 -1 1 x1 0

2 3 0 1 4 x2 0

3 5 -1 1 -1 x3 0

x4

x5

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